Demultiple using up/down separation of towed variable-depth streamer data

ABSTRACT

Methods and systems for processing data acquired using a variable-depth streamer, obtain up-going and down-going wavefields at a predetermined datum, and use them to identify multiples included in the up-going wavefield. An image of a geological formation under the seabed is then generated using the data from which the multiples have been removed, and/or the multiples.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority and benefit from U.S. ProvisionalPatent Application No. 61/894,104, filed Oct. 22, 2013, for “DemultipleUsing Up/down Separation of Towed Variable-depth Streamer Data,” thecontent of which is incorporated in its entirety herein by reference.

BACKGROUND

Technical Field

Embodiments of the subject matter disclosed herein generally relate toprocessing seismic data acquired using a streamer towed to have avariable-depth profile, more specifically, to identifying multiplesincluded in the up-going wavefield using up-going and down-goingwavefields at a predetermined datum.

Discussion of the Background

In seismic acquisition, energy (i.e., a seismic wave) generated by aseismic source propagates downward into a geological formation, and partof the energy is reflected back up. Characteristics of the reflectedenergy detected by seismic sensors are used to produce an image of theearth's reflectivity. In marine data acquisition, the sensors are housedby a streamer towed underwater.

Two types of multiple reflections complicate seismic data processing:water surface-related multiples and inter-bed multiples. Surface-relatedmultiples occur when energy reflected from the subsurface reaches theair-water surface and is reflected back downward into the water columnand the geological formation under the seabed. This energy reflected atthe air-water surface produces a second train of energy reflected fromthe geological formation. Inter-bed multiples are similar, but in thiscase the downward-reflecting surface is a rock interface inside thegeological formation.

Over the years, many methods have been developed to suppress multiples.One method, known as “radon demultiple,” is a modeling approach usuallyin the common midpoint (CMP) domain, where the difference in moveout isused to discriminate between primary energy, which is usually faster,and multiple energy, which arrives later in time. The data is firstnormal-moveout corrected and then a parabolic radon model is generated.In the radon model, primary and multiple energy are distributed ondifferent parabolas which allows for the multiple energy to beidentified and consequently selected. The multiple energy is thenreverse-transformed back to the offset-time domain. Finally, themultiple energy is subtracted from the original input data. The “radondemultiple” method is only effective when moveout discrimination betweenprimary and multiples energy is apparent. Therefore, this method isoften ineffective in shallow water environments or at near offsets.

Another method known as “surface-related multiple elimination” (SRME)uses convolutions and summations to estimate the multiple energy. Withsufficient sampling of sources and receivers, this approach may producea multiple model with the correct kinematic timing. Any amplitude,timing or phase errors are usually subsequently corrected with adaptivesubtraction of the multiple model from the original data. However, theSRME method is difficult to use when the input data is not sufficientlywell spatially sampled. In addition, the SRME method relies on anadaptive subtraction step.

Yet another method known as “deconvolution” may be applied either in theoffset-time or a model (e.g. tau-p) domain. This method builds aprediction operator based on an auto-correlation of the data. Theauto-correlation, which contains energy at the multiples periods, isused to derive a deconvolution operator (based on user parameters) to beapplied to the data. This deconvolution method is often only suitablefor shallow water and for simple structures.

Another method known as “wave-equation modeling” produces a multiplemodel by forward extrapolating seismic reflections into the subsurfaceand back to the receiver datum. The extrapolation step requires areflectivity and velocity model. This method is suitable for modelinglong-period multiples and relies on an adaptive subtraction step as wellas some knowledge of the subsurface (e.g., reflectivity and velocity).

According to yet another method known as “inverse scattering,” amultiple model is predicted by constructing a subseries of thescattering series, which corresponds to the multiples and may be usedfor 2D and 3D multiple prediction. This method is described in thearticle, “An inverse-scattering series method for attenuating multiplesin seismic reflection data,” published in 1997 in Geophysics, 62, No. 6,pages 1975-1989, the content of which is incorporated in its entiretyherein by reference. This method also requires dense source and receiver(i.e., detector) sampling.

As pointed out in the book, “Seismic multiple removal techniques past,present and future,” by Verschuur, D. J., a 2006 EAGE publication, thecontent of which is incorporated in its entirety herein by reference,each of the methods discussed in this section can be ineffective undercertain conditions/environments.

Therefore, multiples removal remains a subject of continuing research,with new opportunities and challenges occurring as data acquisitionsystems evolve, for example, by towing streamers according to a variabledepth profile instead of towing at a substantially constant depth.

SUMMARY

In various embodiments, sea-surface related multiples for data acquiredusing a variable-depth streamer are identified using an up-goingwavefield and a down-going wavefield at a predetermined datum.

According to one embodiment, there is a method for processing dataacquired using a variable-depth streamer. The method includes obtainingan up-going wavefield and a down-going wavefield at a predetermineddatum from the data, using a de-ghosting method. The method furtherincludes identifying multiples based on the up-going wavefield and thedown-going wavefield at the predetermined datum. The method alsoincludes generating an image of a geological formation under the seabedusing data from which the multiples have been removed, and/or themultiples.

According to another embodiment, an apparatus for seismic dataprocessing includes an input-output interface configured to receive dataacquired using a variable-depth streamer and a data processing unit. Thedata processing unit is configured to obtain an up-going wavefield and adown-going wavefield at a predetermined datum from data acquired usingthe variable-depth streamer, to identify multiples based on the up-goingwavefield and the down-going wavefield at the predetermined datum, andto generate an image of a geological formation under the seabed usingdata from which the multiples have been removed, and/or and themultiples.

According to yet another embodiment, there is a computer-readable mediumconfigured to store executable codes which, when executed by a computer,perform a method for processing data acquired using a variable-depthstreamer. The method includes obtaining an up-going wavefield and adown-going wavefield at a predetermined datum from data acquired usingthe variable-depth streamer. The method further includes identifyingmultiples based on the up-going wavefield and the down-going wavefieldat the predetermined datum. The method also includes generating an imageof a geological formation under the seabed using data from which themultiples have been removed, and/or and the multiples.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 is a graph showing frequency distribution of recorded dataacquired with a horizontally-towed streamer;

FIG. 2 is a graph showing frequency distribution of recorded dataacquired with a variable-depth streamer;

FIG. 3 is a diagram illustrating a demultiple method according to anembodiment;

FIG. 4 is a flowchart of a method according to an embodiment;

FIG. 5 is model of wave propagation velocity as a function of depth usedfor simulating data;

FIG. 6A illustrates simulated data, FIG. 6B illustrates an up-goingwavefield at the detection datum, as extracted from the simulated data,and FIG. 6C illustrates a down-going wavefield at the detection datum,as extracted from the simulated data;

FIG. 7A illustrates the up-going wavefield at a predetermined depth (135m), and FIG. 7B illustrates the down-going wavefield at the samepredetermined depth;

FIG. 8A illustrates the up-going wavefield at the seabed, and FIG. 8Billustrates the down-going wavefield at the seabed;

FIG. 9A illustrates the up-going wavefield at the seabed, FIG. 9Billustrates the down-going wavefield at the seabed, FIG. 9C illustratesthe multiples at the seabed which are removed by adaptive subtraction,and FIG. 9D illustrates the data at the seabed after the multiples inFIG. 9C are removed;

FIG. 10 is a schematic diagram of a computing device configured toimplement methods for processing data according to an embodiment; and

FIG. 11 is a flowchart of a method according to another embodiment.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims. The following embodimentsare discussed, for simplicity, with regard to a marine seismic dataacquisition towing a variable-depth streamer. However, similarembodiments and methods may be used for a marine data acquisition systemtowing horizontal streamers and for surveys using electromagnetic waves.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with an embodiment is included in at least oneembodiment of the subject matter disclosed. Thus, the appearance of thephrases “in one embodiment” or “in an embodiment” in various placesthroughout the specification is not necessarily referring to the sameembodiment. Further, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

According to various embodiments, an up-going wavefield and a down-goingwavefield at a predetermined datum are obtained from marine seismicdata. Obtaining these wavefields may be performed using a de-ghostingmethod for marine seismic data acquired using a streamer towed with apredetermined variable-depth profile. Multiples included in the up-goingwavefield are identified using the obtained up-going and down-goingwavefields, and may then be used to generate an image of the geologicalformation under the seabed.

In marine data acquisition systems, a vessel tows a cable called astreamer, which houses seismic wave detectors. The detectors may behydrophones, accelerometers, differential pressure sensors, or othertypes of particle motion sensors. The detectors sense both primaryreflections (i.e., desired energy which has been reflected once from thesubsurface) and multiple reflections (i.e., energy which was reflecteddownward at least once either at the sea surface or within thegeological formation before being recorded at the detectors). A freesurface ghost is the down-going component of the wavefield recordedafter the energy was reflected at the sea surface. Ghosts interfere withup-going primary signals, distorting the bandwidth of the seismic signalrecorded by the detectors (e.g., yielding frequency notches wheninterfering destructively). The frequencies at which these notches occurdepend on the detection depth. FIG. 1 illustrates the frequencydistribution of data acquired with a streamer towed substantiallyhorizontal to the sea surface, at a depth of approximately 7-8 m. Afrequency notch occurs at approximately 100 Hz.

Instead of being towed at a constant depth, streamers can be towed witha predetermined variable-depth profile relative to the water's surface(these streamers are called variable-depth streamers). Frequently(although not exclusively or limiting), a variable-depth streamer has ashallow depth at the near-offsets (closer to the vessel and the seismicsource) and is towed deeper (e.g., up to 50 m) at the far-offsets (e.g.,up to 8,000 m from the streamer's head). By towing the streamer with avariable-depth profile instead of a substantially constant depth, thefrequencies at which ghost reflections distort the seismic signal vary,depending on offsets of individual detectors. This effect is illustratedin the FIG. 2 graph representing frequency distribution of data acquiredwith a variable-depth streamer. Curve 210, which corresponds to adetector at a depth six times the depth of the horizontally towedstreamer whose signal frequency distribution is illustrated in FIG. 1,has six frequency notches between 0-100 Hz. Similarly, curve 220, whichcorresponds to a detector at a depth four times the depth of thehorizontally towed streamer, has four frequency notches between 0-100Hz. Curve 230, which corresponds to a detector at a depth three timesthe depth of the horizontally towed streamer, has three frequencynotches between 0-100 Hz. And curve 240, which corresponds to a detectorat a depth twice the depth of the horizontally towed streamer, has twofrequency notches between 0-100 Hz. When data from all the detectors iscombined, the envelope of the curves is substantially free of ghostnotches. Absence of frequency notches allows for receiver-side ghostremoval and, hence, separation of the recorded data into up-going anddown-going wavefields at the detector. Another advantage of thevariable-depth streamer is that the deeper the detection location, thebetter the signal to noise ratio of the data.

Removing receiver-side ghost reflections (or down-going energy) from thedata acquired using a variable-depth streamer is a form of wavefieldseparation (i.e., recovering up-going and down-going wavefields). Theup-going wavefield contains desirable primary reflections and theremaining multiples whose last bounce is upward toward the detectors.The down-going wavefield contains the ghost reflections.

A method for up-going and down-going wavefield separation ofvariable-depth streamer data using migration and mirror migration datais described in the article, “Deghosting by joint deconvolution of amigration and a mirror migration,” by Soubaras, R., published in 80thSEG Annual Meeting, Expanded Abstracts 29, pp. 3406-3410, 2010, thecontent of which is incorporated in its entirety herein by reference.

In various embodiments described hereinafter, wavefield separation isapplied to the recorded data before migration and typically early in theprocessing flow. This approach is commonly referred to as pre-migrationdeghosting. Any pre-migration deghosting method can be used (e.g.,deghosting using a tau-p model as described in the article,“Pre-migration de-ghosting and re-datuming for variable depth streamerdata,” by G. Poole, SEG Technical Program Expanded Abstracts 2013, pp.4216-4220, and U.S. Patent Application Publication No. 2013/0163376 A1,the contents of which are incorporated in their entirety herein byreference).

Wavefield separation yields the up-going and down-going wavefieldsusable in a demultiple process. Up-going and down-going wavefields arefirst extrapolated from the locus of the variable-depth streamer to apre-determined datum. The location of the pre-determined datum dependson the manner in which removing the multiples (i.e., demultipling) isperformed (some implementation of the demultiple step are discussedlater in this document). Two separate extrapolations are performed: onefor the up-going wavefield and one for the down-going wavefield. In oneembodiment, the up-going wavefield is inverse-extrapolated (i.e.,propagated backward in time) to a pre-determined datum, and thedown-going wavefield is forward-extrapolated (i.e., propagated forwardin time) to the same pre-determined datum. The extrapolated up-going anddown-going wavefields appear to have been recorded at this differentdatum instead of being recorded at a datum determined by thevariable-depth streamer.

The extrapolated data may cover the same shot-receiver offset range asthe input data or may cover a shorter or a larger shot-receiver offsetrange. Extrapolating the data to shorter offsets may enable betterprediction of the near channel multiples. In particular, extrapolationof the up-going wavefield to shorter offsets may improve redatuming ofthe up-going wavefield to the pre-determined datum. In one embodiment,shorter offset data may be extrapolated before the demultiple process,using conventional techniques, e.g., NMO copy, fx extrapolation, sparseRadon extrapolation, etc.

Various extrapolation methods may be used. All extrapolation methodsrequire a velocity model. Since the datum is often preferable within thewater column, only a simple water velocity model may be needed. Notethat the term “water velocity” means the velocity of the wave (sound)propagating through water. Wave-equation methods such as phase-shift(frequency-wavenumber), Kirchhoff (frequency-space) or space-timemethods may be applied to perform the forward and inverse extrapolation.The pre-stack deghosting algorithm (described in U.S. Patent ApplicationPublication No. 2013/0163376 A1) may output the data at a chosen datum,thus combining wavefield separation and extrapolation in a singleoperation.

The seabed is a frequent choice of extrapolation datum because, at thisposition, the receiver-side water-layer multiples in the up-goingwavefield are equal to the down-going wavefield multiplied by thereflection coefficient of the seabed, R. In most surveys, the depth ofthe seabed is well-determined using picked near-offset travel times,using measurements from echo sounders, or information available from anear-offset migration section. Water velocity may be estimated from thedata or measured directly. For example, a Temperature Salinity Dip(TSDIP) device measuring temperature, salinity, and depth may be used todetermine the water velocity using an equation to relate the measuredcharacteristics to the water velocity.

At the seabed, the down-going wavefield may be considered as a model ofthe water-related multiples in the up-going wavefield. As illustrated inFIG. 3, up-going wavefield U(above) (which can be obtained from the dataand then extrapolated at the seabed) is a sum of the up-going wavefieldU(below), which includes the primary reflections, inter-bed multiplesand surface-related multiples whose last upward bounce occurs beneaththe seabed, and the down-going wavefield D(above) multiplied by thereflection coefficient of the seabed, R. Therefore, removing thedown-going wavefield from the up-going wavefield has the effect ofsuppressing all remaining receiver-side water-layer multiples. In oneembodiment, the demultiple step is then expressed as U-RD, where Ucorresponds to the up-going wavefield, D corresponds to the down-goingwavefield, and R is the reflection coefficient of the seabed.

Various methods may be used to subtract the down-going wavefield fromthe up-going wavefield. One embodiment uses straight subtraction, i.e.,the down-going wavefield (scaled by the reflection coefficient R) issubtracted from the up-going wavefield. In another embodiment, thedown-going wavefield (scaled by the reflection coefficient R or not) issubtracted from the up-going wavefield after application of a matchingfilter. The matching filter minimizes the energy between the multiplemodel (down-going wavefield) and the multiples in the data (up-goingwavefield). This procedure is known as an adaptive subtraction, and isoften used when the multiple model does not exactly match the multiplesin the original data. Adaptive subtraction compensates for differencesin arrival time, amplitude and phase between the data and the model.Adaptive subtraction may be used even when the reflection coefficient isnot known or merely estimated. A common minimization criterion is theleast-squares norm, but other possible minimization criteria may be usedand are well-known in the art. Adaptive subtraction is performed in thedomain deemed most suitable, e.g., common-shot domain, common-channeldomain, common-receiver domain, common-slowness domain, curvelet, tau-p,etc.

In one embodiment, instead of using adaptive subtraction with a singlemultiple model, several multiple models may be adaptively subtractedsimultaneously using a method called multi-model adaptive subtraction(which is described in the article, “A Weighted Adaptive Subtraction forTwo or More Multiple Models,” by Y. Mei and Z. Zou, published in SEGTechnical Program Expanded Abstracts 2010: pp. 3488-3492, the content ofwhich is incorporated in its entirety herein by reference). The use ofmulti-model adaptive subtraction has the effect of simultaneouslysubtracting the down-going wavefield and multiples models from othermethods outlined in the “Discussion of the Background” section. In oneembodiment, multi-model adaptive subtraction uses primary protectionbased on an estimate of the primary data; the multi-model adaptivesubtraction then subtracts both primary and multiples models from theinput data so that the output data consists of the residual plus adaptedprimary datasets.

Preferably, subtraction of the down-going wavefield from the up-goingwavefield is not limited to either straight or adaptive subtraction, buta combination of the two. For example, straight subtraction can be anintermediate step yielding an estimate of the local reflectioncoefficient. This intermediate step enables using a scaled version ofthe down-going wavefield (which is the multiple model) in a subsequentadaptive subtraction step. As a further example, straight subtractionmay work well following an adaptive subtraction if the phase of thearrivals is broad. On the other hand, adaptive subtraction may be deemedmore suitable to be applied in a first step if a complex near-surfacedistorts the phase and amplitudes of the arrivals.

As an alternative to the demultiple method just described,surface-related multiples can be removed at the new datum level by anup/down deconvolution. That is, up-going multiples are removed bydividing the up-going wavefield by the down-going wavefield in aspectral domain (e.g., Fourier, Laplace, Z-transform,frequency-wavenumber, tau-p, etc.). The up/down deconvolution haspreviously been applied to ocean-bottom cable data or ocean-bottom datawhere up-going and down-going wavefields are readily available. Theup/down deconvolution has the advantage that no subtraction step isnecessary, but the down-going wavefield must include the direct/incidentarrival. The up/down deconvolution can be performed at the seabed or atanother suitable datum within the water column. Although the up/downdeconvolution does not need to be performed as an alternative to thedemultiple step, it can be used as a preceding or as a subsequent stepthereof to enhance multiples suppression.

Once the primary and multiple datasets at the seabed (or at anotherdatum) are obtained, they can be used in various ways to generate animage of the geological formation under the seabed.

In one embodiment, the primary dataset is extrapolated back to thestreamer locus or other datum. In another embodiment, the primarydataset is extrapolated back to the streamer locus or other datum andused to recreate the ghost energy (re-ghosted).

Alternatively or additionally, the multiple dataset may also beextrapolated back to the streamer locus. In one embodiment, thisextrapolated multiple dataset may be then subtracted from deghosteddata. In another embodiment, the extrapolated multiple dataset is usedto recreate the ghost energy (re-ghosted) and then subtracted from theoriginal data.

In some embodiments, data processing is continued without extrapolatingthe primary and/or multiples to another datum (e.g., at the seabeddatum). In one embodiment, the primary and multiple datasets aremigrated separately, for example, using mirror-migration for themultiples, which may yield an improved illumination, especially for theshallow water data.

In some embodiments, the up-going and down-going wavefields are used ininterferometry (a procedure essentially equivalent to redatuming) forinterpolation and/or extrapolation of the data. In one embodiment,interferometry between the down-going wavefield and a model-basedGreen's function at the seabed yields new traces at shorter offsets thanconventionally considered. In another embodiment, interferometry betweenthe up-going multiple model and a model-based Green's function at thestreamer level generates new traces at shorter offsets thanconventionally considered. Examples of similar procedures are describedin the article, “Interferometric extrapolation of OBS and SSP data,” byDong and Schuster, published in Proceeding of SEG Las Vegas 2008 AnnualMeeting, pp. 3013-3017, the content of which is incorporated in itsentirety herein by reference. Extending the data to shorter offsets hasthe effect of an increased aperture used for imaging. Other combinationsbetween up-going and down-going wavefields are foreseeable forinterpolation/extrapolation purposes.

Any subtraction steps combined in the above primary and multipledatasets processing for generating an image of the geological formationunder the seabed may be straight subtraction or adaptive subtraction, aspreviously discussed.

FIG. 4 is a flowchart of a method 400 for processing data acquired usinga variable-depth streamer. Method 400 includes obtaining an up-goingwavefield and a down-going wavefield at a predetermined datum from thedata acquired using the variable-depth streamer, at 410. A de-ghostingmethod may be used to obtain the up-going and down-going wavefields.Towing a variable-depth streamer (instead of a substantially horizontalstreamer) provides receiver ghost diversity, thus increasing andextending the usable seismic bandwidth. This is advantageous forsubsequent imaging and inversion applications. Towing deep at thefar-offsets (i.e., at a great distance from the source) increases thesignal-to-noise ratio and, thus, data can be acquired in areas where theweather window is limited.

Method 400 further includes identifying multiples included in theup-going wavefield based on the up-going wavefield and the down-goingwavefield at the predetermined datum, at 420. Decomposing the data intoan up-going wavefield and a down-going wavefield is another benefit ofvariable-depth acquisition, and it is particularly advantageous foridentifying and/or removing multiples, as previously discussed. Up-goingand down-going wavefields may be used in various applications withrespect to interpolation and extrapolation. In particular, isolating thedown-going wavefield is useful for identifying and/or removing multiplesbecause variations in the sea-surface state, such as wave height andreflection coefficient, are appropriately taken into consideration.

Method 400 also includes generating an image of a geological formationunder the seabed using data from which the multiples have been removed,and/or the multiples, at 430. As already mentioned, multiples removalcan be achieved by up/down deconvolution. This is advantageous becausesince surface-related multiples are removed by a deconvolution process,adaptive subtraction is no longer necessary.

A one-dimensional (depth-only) velocity model is illustrated in FIG. 5.A source is fired at 5 m and recordings are made at a streamer towed atabout 15 m depth. The maximum offset is 1,500 m. For simplicity, thisillustration does not simulate data acquired using a variable-depthstreamer, but the above-described embodiments can also be used formeasurements acquired with streamers towed substantially horizontal(i.e., at a constant depth). The acquired data (pressure amplitudeversus time and offset) is illustrated in FIG. 6A where the timeincreases downward, offsets (i.e., distances from the source) increasefrom left to right, and amplitude is represented by different shades ofgray, white and black corresponding to opposite phases of the maximumamplitude.

Data in FIG. 6A is decomposed into an up-going wavefield (illustrated inFIG. 6B) and a down-going wavefield (illustrated in FIG. 6C) at thereceiver-side using methods known in the art. The graphs in FIGS. 6B and6C are represented in the same style (i.e., axes and amplitudecorrelated with the shades of gray) as FIG. 6A. The up-going wavefieldis free of receiver-side ghosts.

The up-going wavefield in FIG. 6B is extrapolated backward in time to adatum at 135 m depth in the water column and illustrated in FIG. 7A. Thedown-going wavefield is extrapolated forward in time to the same datumat 135 m depth in the water column and illustrated in FIG. 7B. Thewavefields are extrapolated using a frequency-wavenumber phase shiftalgorithm using a water velocity equal to 1,500 m/s, but other methodsmay be used. Comparing FIGS. 6B and 6C with FIGS. 7A and 7B, oneobserves that the water-layer-related multiples begin to align in time.For example, the second-arrival in FIG. 7A, which corresponds to afirst-order multiple reflected from the first interface, almost overlapsthe equivalent arrival in FIG. 7B.

Applying an up/down deconvolution using these up-going and down-goingwavefields (i.e., corresponding to the datum at 135 m depth illustratedin FIGS. 7A and 7B) results in removing all receiver-side water layermultiples from the up-going wavefield. Note when applying thedeconvolution, the incident (i.e., direct) wavefield is included in thedown-going wavefield. This incident wavefield is not illustrated inFIGS. 6C and 7B.

Instead of using a datum at 135 m depth, the up-going and down-goingwavefields may be extrapolated at the seabed (i.e., at 200 m depth).FIG. 8A illustrates the up-going wavefield in FIG. 6B after beingextrapolated to the seabed. FIG. 8B illustrates the down-going wavefieldin FIG. 6C after being extrapolated to the seabed. One observes that thereceiver-side water-layer multiples align in the up-going and down-goingwavefields.

FIGS. 9A-9D illustrate identification and removal of the multiples atthe seabed. FIG. 9A is the same as FIG. 8A, representing the up-goingwavefield at the seabed. FIG. 9B represents a scaled down-going field atthe seabed, i.e., the down-going wavefield multiplied by the reflectioncoefficient (e.g., 0.49). FIG. 9C illustrates the multiples obtained by(adaptively) subtracting the scaled down-going wavefield at the seabed(in FIG. 9B) from the up-going wavefield at the seabed (in FIG. 9A).Specifically (but not limiting), the subtraction was performed using aleast-squares norm matching filter in the shot domain.

FIG. 9D represents the demultipled up-going wavefield (i.e., primaryreflections, inter-bed multiples and remaining free-surface multiples)at the seabed, i.e., the difference between the up-going wavefield inFIG. 9A and the multiples in FIG. 9C. This demultipled up-goingwavefield and/or the multiples may then be extrapolated back to theoriginal datum (i.e., the locus of the variable-depth streamer when datawas acquired), in this example to 15 m depth, or at another datum forsubsequent processing, in order to generate the image of the geologicalformation under the seabed.

While the description predominantly refers to 2D algorithms, 3Dimplementations of the deghosting and extrapolation may also be used. Inaddition, the wavefield separation may make use of a variable depthstreamer equipped with multi-component sensors; i.e. particle motion(e.g. acceleration, velocity, differential pressure) in addition tohydrophone recordings.

FIG. 10 is a schematic diagram of a computing device 1000 configured toimplement methods for processing data according to an embodiment.Hardware, firmware, software or a combination thereof may be used toperform the various steps and operations of the above-described methods.The computing device 1000 may include a server 1001, which has a centralprocessor (CPU) 1002 coupled to a random access memory (RAM) 1004 and toa read-only memory (ROM) 1006. The ROM 1006 may also be other types ofstorage media to store programs, such as programmable ROM (PROM),erasable PROM (EPROM), etc. The CPU 1002 communicates with otherinternal and external components through input/output (I/O) circuitry1008 and bussing 1010, to receive the data acquired using avariable-depth streamer and output one or more of the multiples, theprimaries and/or the image of the geological formation. The processor1002 carries out a variety of functions as are known in the art, asdictated by software and/or firmware instructions.

The server 1001 may also include one or more data storage devices,including hard drives 1012, CD-ROM drives 1014, and other hardwarecapable of reading and/or storing information such as DVD, etc. In oneembodiment, software for carrying out the above-discussed methods may bestored and distributed on a CD-ROM or DVD 1016, a USB storage device1018 or other form of media capable of portably storing information.These storage media may be inserted into, and read by, devices such asthe CD-ROM drive 1014, the disk drive 1012, etc. Server 1001 may becoupled to a display 1020, which may be any type of known display orpresentation screen, such as LCD, plasma display, cathode ray tubes(CRT), etc. The image of the geological formation or graphs similar tothe ones in FIGS. 5-8 may be shown on display 1020. A user inputinterface 1022 is provided and may include one or more user interfacemechanisms such as a mouse, keyboard, microphone, touchpad, touchscreen, voice-recognition system, etc.

Server 1001 may be coupled to other devices, such as sources, detectors,etc. The server may be part of a larger network configuration as in aglobal area network (GAN) such as the Internet 1028, which allowsultimate connection to various landline and/or mobile computing devices.

FIG. 11 is a flowchart of a method 1100 for exploring a geologicalformation under the seabed according to yet another embodiment. Method1100 includes acquiring data using a variable-depth streamer at 1110.Method 1100 further includes processing the data to generate an image ofthe geological formation at 1120. The processing of the data includesidentifying multiples based on an up-going wavefield and a down-goingwavefield at a predetermined datum. The up-going wavefield and thedown-going wavefields may be derived using an inversion and/orminimization method. Alternatively, the up-going wavefield and thedown-going wavefields may be obtained using a de-ghosting method.

The disclosed embodiments enable processing marine seismic data thatidentify multiples based on up-going and the down-going wavefields. Itshould be understood that this description is not intended to limit theinvention. On the contrary, the exemplary embodiments are intended tocover alternatives, modifications and equivalents, which are included inthe spirit and scope of the invention as defined by the appended claims.Further, in the detailed description of the exemplary embodiments,numerous specific details are set forth in order to provide acomprehensive understanding of the claimed invention. However, oneskilled in the art would understand that various embodiments may bepracticed without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone without the other features andelements of the embodiments or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

What is claimed is:
 1. A method for processing recorded data acquiredusing a variable-depth streamer, the method comprising: receiving therecorded data acquired using the variable-depth streamer; applyingwavefield separation to the recorded data using a processor, at a locusof the variable-depth streamer, to obtain an up-going wavefield and adown-going wavefield at the locus of the variable-depth streamer;extrapolating the up-going wavefield and the down-going wavefield fromthe locus of the variable-depth streamer to a predetermined datum,different from the locus of the variable-depth streamer; calculatingmultiples by removing the extrapolated down-going wavefield at thepredetermined datum from the extrapolated up-going wavefield at thepredetermined datum; removing the multiples from the extrapolatedup-going wavefield at the predetermined datum to obtain a primarydataset, which is then migrated or extrapolated to another datum; andgenerating an image of a geological formation under the seabed using (1)the primary dataset, and/or (2) the multiples.
 2. The method of claim 1,wherein the predetermined datum is the seabed.
 3. The method of claim 1,wherein the extrapolated up-going wavefield and the extrapolateddown-going wavefield at the predetermined datum are obtained using awavefield separation based on a tau-p model thereof.
 4. The method ofclaim 1, wherein the extrapolation uses information on a water velocitydependence on depth.
 5. The method of claim 1, wherein the extrapolatedup-going wavefield and the extrapolated down-going wavefield at thepredetermined datum are obtained using a sparse inversion method.
 6. Themethod of claim 1, wherein the calculating of the multiples includesdetermining a matching filter that minimizes a difference between theextrapolated up-going wavefield and the extrapolated down-goingwavefield at the predetermined datum.
 7. The method of claim 1, whereinthe calculating of the multiples is an iterative process.
 8. The methodof claim 7, wherein the iterative process uses at least two differentmethods to identify the multiples.
 9. The method of claim 1, wherein thecalculating of the multiples includes: transforming in a spectral domainthe extrapolated up-going wavefield and the extrapolated down-goingwavefield at the predetermined datum; and dividing the transformedup-going wavefield to the transformed down-going wavefield.
 10. Themethod of claim 1, further comprising: extrapolating the multiples toanother datum.
 11. The method of claim 1, further comprising: migratingthe multiples separately from the primary dataset, to another datum. 12.An apparatus for seismic data processing, the apparatus comprising: aninput-output interface configured to receive recorded data acquiredusing a variable-depth streamer; and a data processing unit configuredto apply wavefield separation to the recorded data, at a locus of thevariable-depth streamer, to obtain an up-going wavefield and adown-going wavefield at the locus of the variable-depth streamer; toextrapolate the up-going wavefield and the down-going wavefield from thelocus of the variable-depth streamer to a predetermined datum, differentfrom the locus of the variable-depth streamer; to calculate multiples byremoving the extrapolated down-going wavefield at the predetermineddatum from the extrapolated up-going wavefield at the predetermineddatum, and to generate an image of a geological formation under theseabed using (1) a primary dataset obtained by removing the multiplesfrom the extrapolated up-going wavefield at the predetermined datum,and/or (2) the multiples wherein the data processing unit is configuredto perform one or more of the following operations to generate theimage: extrapolating the multiples to another datum; extrapolating theprimary dataset to the another datum; and migrating the primary datasetand the multiples separately, to the another datum.
 13. The apparatus ofclaim 12, wherein the predetermined datum is the seabed.
 14. A methodfor exploring a geological formation under the seabed, the methodcomprising: receiving data recorded using a variable-depth streamer;processing the recorded data to generate an image of the geologicalformation using a processor, wherein the processing includes, applyingwavefield separation to the recorded data, at a locus of thevariable-depth streamer, to obtain an up-going wavefield and adown-going wavefield at the locus of the variable-depth streamer,extrapolating the up-going wavefield and the down-going wavefield fromthe locus of the variable-depth streamer to a predetermined datum,different from the locus of the variable-depth streamer, calculatingmultiples based on the extrapolated up-going wavefield and theextrapolated down-going wavefield at the predetermined datum, theup-going wavefield and the down-going wavefields at the locus of thevariable-depth streamer being derived using an inversion and/orminimization method, removing the multiples from the extrapolatedup-going wavefield at the predetermined datum to obtain a primarydataset, which is then migrated or extrapolated to another datum, andgenerating an image of the geological formation under the seabed using(1) the primary dataset, and/or (2) the multiples.
 15. A non-transitorycomputer-readable medium configured to store executable codes which whenexecuted by a computer perform a method for processing recorded dataacquired using a variable-depth streamer, the method comprising:receiving the recorded data acquired using the variable-depth streamer;applying wavefield separation to the recorded data, at a locus of thevariable-depth streamer, to obtain an up-going wavefield and adown-going wavefield at the locus of the variable-depth streamer;extrapolating the up-going wavefield and the down-going wavefield fromthe locus of the variable-depth streamer to a predetermined datum,different from the locus of the variable-depth streamer; calculatingmultiples by removing the extrapolated down-going wavefield at thepredetermined datum from the extrapolated up-going wavefield at thepredetermined datum; removing the multiples from the extrapolatedup-going wavefield at the predetermined datum to obtain a primarydataset, which is then migrated or extrapolated to another datum; andgenerating an image of a geological formation under the seabed using (1)the primary dataset, and/or (2) the multiples.